Math 124 (Pezzoli)
Fall 2015
Midterm #2 (80 points)
Name
TA:
.
Section:
Instructions:
• Your exam should contain 4 problems and 6 pages; please make sure you have a complete exam.
• Box in your final answer when appropriate.
• Your work needs to be neat and legible.
• You MUST show work for credit. No credit for answers only.
√
• Unless otherwise instructed, ALWAYS GIVE YOUR ANSWERS IN EXACT FORM. For example, π, 2, ln(2)
are in exact form; the corresponding approximations 3.1415, 1.4142, 0.6931 are NOT in exact form.
• You are allowed one 8.5 × 11 sheet of notes (both sides). Make sure your calculator is in radian mode.
Problem #1 (15 pts)
Problem #2 (15 pts)
Problem #3 (15 pts)
Problem #4 (15 pts)
TOTAL (60 pts)
1
2015-11-30 21:41:54
1/5
124mid2grading (#14)
Problem 1 Compute the derivatives of the following functions. You do not need to simplify.
a)
!
"x3 +x−1
!#
3x + 2
x−1
x
(5 points)f (x) =
2
b) (5 points) h(x) = ln
"
.
c) (5 points) y(x) defined by the implicit equation xy2 +yx2 = 2 (your answer should be an expression
in x and y) .
2
2015-11-30 21:41:54
2/5
124mid2grading (2/5)
2
Problem 2 (15 points) Use linear approximation to estimate
(8.2) 3 . Give an exact answer.
Do you think the estimate you have calculated above is an underestimate or an overestimate ? Justify
your answer.
3
2015-11-30 21:41:54
3/5
124mid2grading (3/5)
Problem 4 (15 points) A curve C has parametric equations:
x = t2 + 3t
y = t2 + 2t + 2
for −∞ < t < ∞.
(a) Find the equations of all the tangents to C that pass through the point Q = (0, 1).
(b) Find all points P on the curve such that the tangent line at P is horizontal.
4
2015-11-30 21:41:54
4/5
124mid2grading (4/5)
Problem 4 (15 points) A street light is mounted at the top of a 15-feet tall pole. An ice sculpture is being moved
away from the pole with a speed of 3 feet/min along a straight path. The ice sculpture is slowly melting
and its height decreases at a constant rate of 0.2 feet / min. How fast is the tip of the sculpture’s
shadow moving, when the sculpture is 10 feet from the pole and has a height of 5 feet ?
5
2015-11-30 21:41:54
5/5
124mid2grading (5/5)